Abstract
In this paper, a new approach to the issue of extra-logical information within analytic (i.e. obeying the sub-formula property) sequent systems is introduced. We prove that incorporating extra-logical axioms into a purely logical system can preserve analyticity, provided these axioms belong to a suitable class of formulas that can be decomposed into a set of equivalent initial sequents and are permutable over the cut rule. Our approach is applicable not only to first-order classical and intuitionistic logics, but also to substructural logics. Furthermore, we establish a limit for the augmented systems under analysis: exceeding the boundaries of their respective classes of extra-logical axioms leads to either a loss of analyticity or a loss of structural properties.
Matteo Tesi
PostDoc Researcher (Marie Curie Individual Fellowship)
Matteo’s research focuses on non-classical (modal, intermediate, and substructural) logics, structural proof theory and their philosophical applications. He has worked with sequent calculi and their generalizations (hypersequents, nested sequents, and labelled sequents) to offer analytic presentations of families of non-classical logics.